Post-Quantum Cryptography in Blockchain

• Post-quantum cryptography in blockchain is a discipline that replaces quantum-vulnerable digital signatures and hash functions with schemes based on lattice, code, and multivariate systems.
• Integrating PQC entails significant trade-offs, including larger key/signature sizes and altered throughput, which necessitate protocol redesign and off-chain storage strategies.
• Adopting PQC in blockchain requires hybrid deployment, signature aggregation, and recalibration of block parameters to secure consensus and maintain network efficiency.

Post-quantum cryptography (PQC) in blockchain is the science and engineering of integrating cryptographic mechanisms that remain secure against quantum adversaries into distributed ledger protocols. Blockchains heavily depend on digital signature algorithms, hash functions, and, in some deployments, encryption and zero-knowledge proof systems—all of which face fundamental security breakdowns in the face of practical quantum computers. Shor’s algorithm directly compromises the discrete logarithm (ECDSA, EdDSA, BLS), integer factorization (RSA), and pairing-based cryptography underpinning consensus, identity, and zero-knowledge protocols. Grover’s algorithm gives quadratic speedup against hash-based constructions, reducing their collision and preimage resistance. PQC mitigates these threats by replacing quantum-vulnerable primitives with schemes based on harder mathematical problems—most notably those rooted in lattice theory, code-based cryptography, multivariate polynomials, and hash-based constructions. The result is a new suite of blockchain architectures with modified performance, incentive, consensus, and storage characteristics that differ fundamentally from their classical predecessors (Mallick et al., 15 Dec 2025).

1. Quantum Threats and Legacy Blockchain Vulnerabilities

Quantum computing poses existential risks to the cryptographic foundations of modern blockchains. Shor’s algorithm solves the discrete logarithm and factoring problems in polylogarithmic time, rendering ECDSA, RSA, EdDSA, BLS12-381, and pairing-based SNARK/VRF constructions trivially forgeable (Mallick et al., 15 Dec 2025, Mutha et al., 24 Aug 2025, Baseri et al., 21 Jan 2025). This collapses the authenticity and integrity guarantees of all permissionless and permissioned blockchains whose transaction or consensus layers are tied to these assumptions.

Hash-based PoW algorithms (e.g., double-SHA-256 in Bitcoin) are not immune: Grover’s algorithm reduces n-bit search complexity from $2^n$ to $2^{n/2}$, making 51% or chain-rewrite attacks more plausible unless hash sizes are doubled or mining targets are dynamically recalibrated. The ramifications are extensive:

• Transaction signature forgeries, chain reorganizations, double-spending (Schemitt et al., 10 Oct 2025, Chen, 23 Jan 2024).
• Progressive breakdown of ZK-SNARK-based privacy mechanisms dependent on ECDLP-based pairings (Yang et al., 2 Sep 2024).
• Elevated risks of orphaned blocks (forks) due to slower block propagation stemming from increased signature and proof sizes (Mallick et al., 15 Dec 2025).

2. Post-Quantum Cryptographic Primitives for Blockchain

NIST-standardized PQC algorithms represent the dominant direction for post-quantum blockchains. The leading candidate families are:

Family	Example Schemes	Key Size (PK/SK)	Signature/Ciphertext	Security Notion
Lattice-based	Dilithium, Kyber, Falcon	1–4 KB	666 B–4.6 KB	Module-LWE, NTRU-SIS hard
Code-based	HQC, Classic McEliece	1MB–>10MB	1–2 KB (KEM)	Syndrome decoding hard
Hash-based	SPHINCS+	32–64 B (PK)	8–41 KB	Hash preimage/collision resistance
Multivariate	UOV, Rainbow, MAYO	1–1000+ KB	40–1000 B	MQ-system inversion hard

Signature sizes for PQC are typically 20–50× larger than classical ECDSA/EdDSA signatures (~64–73 B), with Dilithium2 yielding 2420 B, Falcon-512 666 B, and SPHINCS+ up to 41 KB (Mallick et al., 15 Dec 2025, Schemitt et al., 10 Oct 2025, Chhetri et al., 12 Oct 2025). KEMs such as Kyber and HQC provide 768 B–1 MB ciphertexts and keys, supporting quantum-resilient encrypted channels for off-chain and consensus communications.

The selection of PQC primitives entails complex trade-offs: lattice-based schemes strike the most favorable balance between signature/key size, computational efficiency, and quantum security margin (Ghosh, 18 Jul 2025, Fernandez-Carames et al., 1 Feb 2024). Code-based schemes incur massive key sizes except in specialized KEM-only roles; hash-based approaches provide maximal conservatism but at prohibitive signature overhead for high-throughput ledgers (Mallick et al., 15 Dec 2025, Fernandez-Carames et al., 1 Feb 2024).

3. Integration Patterns and Blockchain Architectural Redesign

Naïvely swapping out quantum-vulnerable schemes with PQC introduces intolerable overheads for storage, bandwidth, and protocol liveness. Careful architectural adaptation is therefore mandatory (Mallick et al., 15 Dec 2025, Chhetri et al., 12 Oct 2025, Baseri et al., 21 Jan 2025). Key integration approaches include:

• Signature Aggregation: Batch-verification and multi-instance combining (e.g., lattice-based signature aggregation or STARK-style batching), reducing signature volume from $n s$ to $s + O(\log n)$ per block (Mallick et al., 15 Dec 2025, Chhetri et al., 12 Oct 2025).
• Merkle-Tree Compression: Block headers store a Merkle root over signatures; nodes fetch proof paths for individual verification, amortizing transmission and on-chain storage (Mallick et al., 15 Dec 2025).
• Hybrid and Dual-Signature Transactions: Blocks and transactions may carry both a classical and a PQ signature during the migration phase, ensuring backward compatibility and cryptographic agility (Chhetri et al., 12 Oct 2025, Baseri et al., 21 Jan 2025, Holcomb et al., 2020).
• Block Parameter Recalibration: Throughput and propagation delay are bounded by the increased size of signatures. Block size ($B_{\max}$), block time ($T_b$), and transaction inclusion logic (e.g., fill ratio $\eta = r \cdot s/B_{\max}$) must be recomputed to avoid elevated fork rates—tenfold increases in signature sizes can raise Bitcoin’s fork probability from 1.9% to 17.6% (Mallick et al., 15 Dec 2025).
• Selective Off-Chain Storage: Bulk signatures and public keys may be stored off-chain in a content-addressed system (e.g., IPFS), with only succinct hashes or commitments on-chain, reducing per-transaction storage impact (Al-Janabi, 23 Aug 2025, Mallick et al., 15 Dec 2025).
• Permissioned Blockchains: Protocols such as PQFabric integrate PQC at the certificate (PKI/MSP) layer using hybrid X.509 structures, dual-layer certificate signing, and crypto-agile software stacks (Holcomb et al., 2020).
• Consensus Modifications: PoW schemes with memory-hard puzzles or (for proof-of-stake/BFT) PQC-mode threshold signatures secure block production and validator voting (Chen et al., 2020, Gurung et al., 2023, Mutha et al., 24 Aug 2025).

4. Performance, Scalability, and Storage Implications

The migration to post-quantum signatures and KEMs causes substantial increases in on-chain and network resource demands:

Metric	ECDSA Baseline	Dilithium2	Falcon-512	SPHINCS+ 128f
Sig Size	~64–73 B	2,420 B	666 B	~41,000 B
Key Size	~32 B (PK)	1,312 B (PK)	897 B (PK)	32 B (PK)
Throughput	~4000 TPS (1 MB)	~3700 TPS	~3850 TPS	~900 TPS
Node Storage	Baseline	20–50× growth	10× growth	>200× growth

A 1 MB Bitcoin block using ECDSA (~7,600 tx/block) drops to ~400 tx/block with SPHINCS+-based signatures due to size constraints (Schemitt et al., 10 Oct 2025, Mallick et al., 15 Dec 2025). Minimum signature-verification times for lattice-based schemes (Dilithium, Falcon) are sub-millisecond and can even outperform ECDSA at high security levels (Schemitt et al., 10 Oct 2025). However, storage, archiving, and full-node bootstrapping costs scale multiplicatively with chain age and transaction volume, challenging decentralization and increasing the risk of validator centralization (Mallick et al., 15 Dec 2025, Baseri et al., 21 Jan 2025).

Protocol-level mitigations include block-size limit increases, at the cost of higher propagation latency and consequent fork risks, and the deployment of cryptographic hardware accelerators (AVX2, FPGA, ASIC) for PQC arithmetic (Chhetri et al., 12 Oct 2025, Al-Janabi, 23 Aug 2025).

5. Consensus, Incentives, and Trust-Model Evolution

PQC impacts blockchain economics and incentive structures fundamentally. Increased validator and miner costs (bandwidth, CPU, storage) drive up the minimum viable node resource level, which in turn encourages centralization unless transaction fees and gas prices internalize the true marginal cost of PQ operations (Mallick et al., 15 Dec 2025, Baseri et al., 21 Jan 2025). For PoW, the exponential growth in stale/forked block probability at large signature volumes incentivizes miners to self-limit block sizes, optimizing: $\max_B\,(1-\pi(B))\cdot F(B)$ where $\pi(B)$ is fork probability and $F(B)$ the fee function.

In PoS or BFT systems, the overhead per validator for signature verification and communication grows with committee size and block volume (Chhetri et al., 12 Oct 2025, Gurung et al., 2023). Reputation systems may preferentially penalize high-latency nodes; practitioners must track network propagation and miner behavior as PQ rollout progresses (Mallick et al., 15 Dec 2025, Ghosh, 18 Jul 2025).

6. Security and Migration Strategies

Transitioning to PQC is not atomic; coordinated, multi-phase rollouts are required:

1. Inventory all cryptographic uses on- and off-chain (Chhetri et al., 12 Oct 2025, Baseri et al., 21 Jan 2025).
2. Begin hybrid deployments, supporting both classical and PQC algorithms.
3. Test PQC performance and block-level propagation on testnets, recalibrating block and gas limits (Mallick et al., 15 Dec 2025, Mutha et al., 24 Aug 2025).
4. Incrementally enforce PQC signatures/keys via dual-signature blocks or transaction types.
5. Complete cut-over at a predetermined block height, deprecating classical cryptography.

Security proofs and hardening measures are essential. PQC must satisfy formal post-quantum unforgeability—e.g., for Dilithium/ML-DSA: $$\Pr[\mathcal{A}\ \text{forges a valid PQ signature}]\leq\varepsilon(n)$$ for $\mathcal{A}$ running in time $\mathrm{poly}(n)$, under LWE hardness (Mallick et al., 15 Dec 2025). Additional attention is required for side-channel resistance, algorithm diversification, and crypto-agility for future-proof updates (Chhetri et al., 12 Oct 2025, Al-Janabi, 23 Aug 2025).

7. Open Problems and Research Frontiers

Key outstanding challenges include:

• Development of aggregate PQC signatures and efficient batch-verification frameworks (Mallick et al., 15 Dec 2025, Chhetri et al., 12 Oct 2025).
• Mitigating the storage/propagation load (e.g., off-chain storage, signature compression) (Mallick et al., 15 Dec 2025, Ghosh, 18 Jul 2025).
• Lightweight PQC signatures (<512 B) to fit strict block size and transaction bottlenecks (Chhetri et al., 12 Oct 2025).
• Quantum-safe zero-knowledge proofs (e.g., zk-STARKs, lattice-based ZKPs) tailored for blockchain applications (Yang et al., 2 Sep 2024, Chhetri et al., 12 Oct 2025).
• Formal governance, mature PKI integration, and algorithm-parameter agility frameworks for longitudinal upgradeability (Chhetri et al., 12 Oct 2025, Baseri et al., 21 Jan 2025).
• Post-quantum consensus primitives, memory-hard PoW, and adaptation of validator selection procedures to future adversarial models (Chen et al., 2020, Mutha et al., 24 Aug 2025).

In sum, robust PQC integration is now an unavoidable technical and operational prerequisite for blockchains seeking to maintain decentralized trust in a quantum-capable adversarial landscape (Mallick et al., 15 Dec 2025, Chhetri et al., 12 Oct 2025, Fernandez-Carames et al., 1 Feb 2024). The field remains under intense study, with engineering best-practices and standardization rapidly maturing toward production-grade, quantum-resilient distributed ledgers.